What is the I Ching?
Sixty-four pictures — and the arithmetic underneath them.
The I Ching (周易 · 주역, the Book of Changes) answers a question with a picture instead of a sentence. The picture is six lines stacked from the bottom up, each one either whole or broken, which makes sixty-four figures in all. Some lines are “moving” — they are on the point of turning into their opposite — so a cast usually shows you two figures at once: the one you are standing in, and the one it is turning into. Nothing in it is a yes or a no. It is an image to sit with, and the sitting is the point.
Two methods, kept strictly apart, because they belong to two different schools and mixing them makes both untrue. The hexagram waiting for you each day is cast by 매화역수 (Plum Blossom Yi): plain arithmetic on two numbers — upper trigram = n₁ mod 8, lower = n₂ mod 8, moving line = (n₁+n₂) mod 6. No randomness, exactly one moving line, and the same person sees the same figure all day. Asking a question uses the older yarrow-stalk method (시초점). Bokki performs the hand procedure itself in code: start from forty-nine stalks, then 分二 split them in two, 掛一 hang one aside, 揲四 count off by fours, 歸奇 set the remainder apart. Three of those make one line; six lines take eighteen.
Because the stalks make them lopsided, and the lopsidedness is the teaching. Run that arithmetic and a line comes out old yin 1/16, young yang 5/16, young yin 7/16, old yang 3/16. Those are not numbers we dialled in; they fall out of the counting. So a yang line changes three times as often as a yin line — yang moves, yin stays. Three tossed coins give a tidy symmetric 1:3:3:1 and quietly delete that idea. Bokki used coins once and stopped. A test rolls a hundred thousand casts to make sure the distribution has not drifted.
Casting is half the work; knowing where to look is the other half, and that rule comes from Zhu Xi (朱子), 『역학계몽』, the chapter 「고변점」. No moving lines: read the primary figure's judgment. One: that line's text. Two: both, with the upper as the main one. Three: both judgments, with the primary as the main one. Four: the two unchanged lines of the resulting figure, the lower one main. Five: its single unchanged line. Six: 用九 if the primary is 乾 and 用六 if it is 坤, otherwise the resulting figure's judgment. Bokki takes the casting odds from the same book, so one screen never mixes two lineages.
All sixty-four judgments and all three hundred and eighty-four line texts are in the engine, checked character by character against the received 통행본 text, with the phrasing (句讀) following 朱熹 『周易本義』 wherever the schools disagree. The English and Korean renderings are our own — we worked from the classical Chinese rather than copying a modern version, because the classic is public domain but a translation is somebody else's work. Those renderings exist in Korean and English only right now; other languages are shown the English.
It will not tell you yes or no, and it will not put a percentage on anything. It does not do 육효 — the Han-dynasty 납갑 method that fixes stems and elements to each of the six lines and aims at “will it happen, and when”. That is a different school, and we have not built it. There is also one gap inside the rule we did adopt: 『역학계몽』 splits the twenty three-moving-line cases into a first ten and a last ten, and which half you land in flips whether the primary or the resulting figure leads. The ordering behind that split belongs to a table we cannot reconstruct with confidence, so Bokki always treats the primary as the main one and says so rather than guessing. And asking the same question twice returns the same answer: 蒙卦 says 初筮告 再三瀆 瀆則不告 — the first asking is answered, the second and third are an intrusion — so a repeat is handed back from memory instead of recast.